Finite Group Databasebeta

← #26233892

Subgroups — #26233892

Order 12032.

686 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252045C211yesmaximal, characteristic
2#20252043C211yesmaximal, characteristic
3#20251976C211yesmaximal, characteristic
4#20244140C211yesmaximal, characteristic, complemented
5#20244133C211yesmaximal, characteristic, complemented
6#20243989C211yesmaximal, characteristic, complemented
7#20243988C211yesmaximal, characteristic, complemented
8#20243986C211yesmaximal, characteristic, complemented
9#20243486C211yesmaximal, characteristic
10#20243486C211yesmaximal, characteristic
11#20243429C211yesmaximal, characteristic
12#20243271C211yesmaximal, characteristic, complemented
13#20243268C211yesmaximal, characteristic, complemented
14#20243170C211yesmaximal, characteristic
15C47×#1922C211yesmaximal, characteristic, complemented
16C22×#10625324C2211yescharacteristic
17#117×D47C2211yescharacteristic
18#117×D47C2211yescharacteristic
19#15689185—21no—
20#15689183—21no—
21#15689183—21no—
22#15689182—21no—
23#15689179—21no—
24#15689178—21no—
25#15689175—21no—
26#15689174—21no—
27C2×#13093959C2211yescharacteristic
28C2×#13093959C2211yescharacteristic
29#15689164C411yescharacteristic, complemented
30#15689164C411yescharacteristic, complemented
31#15689164C411yescharacteristic, complemented
32#15689164C411yescharacteristic, complemented
33#15689162C411yescharacteristic, complemented
34#15689162C411yescharacteristic, complemented
35#15689162C411yescharacteristic, complemented
36#15689162C411yescharacteristic, complemented
37#15689161C2211yescharacteristic
38#15689159C2211yescharacteristic
39#15689159C2211yescharacteristic
40#15689151C2211yescharacteristic
41#15689150C2211yescharacteristic
42#15689149C2211yescharacteristic
43#15689086C2211yescharacteristic
44#15689086C2211yescharacteristic
45C2×(C2×D47)⋊C8C2211yescharacteristic
46#15689081C2211yescharacteristic
47#15689079C2211yescharacteristic
48#15689078C2211yescharacteristic
49C2×#13093935C2211yescharacteristic
50C2×C8×Dic47C2211yescharacteristic
51C4×(C2×D47)⋊C4C2211yescharacteristic
52#15688888C2211yescharacteristic
53#15688884C2211yescharacteristic
54#15688884C2211yescharacteristic
55#15688883C2211yescharacteristic
56#15688883C2211yescharacteristic
57#15688882C2211yescharacteristic
58#15688882C2211yescharacteristic
59#15688877C2211yescharacteristic
60C47×#427C2211yescharacteristic
61C47×#424C2211yescharacteristic
62C47×#405C2211yescharacteristic
63C47×#341C2211yescharacteristic
64C47×#339C2211yescharacteristic
65C47×#339C2211yescharacteristic
66C47×#336C2211yescharacteristic
67C22×C4×D47C2311yescharacteristic
68C2×#10625329C2311yescharacteristic
69C2×#10625329C2311yescharacteristic
70C2×#10625324—22no—
71C2×#10625324—22no—
72C2×#10625324C2×C411yescharacteristic
73C2×#10625324C2×C411yescharacteristic
74C2×#10625324C2×C411yescharacteristic
75C2×#10625324C2×C411yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78#13093983C2311yescharacteristic
79#13093983C2311yescharacteristic
80#13093982C2×C411yescharacteristic
81#13093982C2×C411yescharacteristic
82#13093982C2×C411yescharacteristic
83#13093982C2×C411yescharacteristic
84#13093981—21no—
85#13093981—21no—
86#13093980—21no—
87#13093980—21no—
88C4⋊C4×D47C2×C411yescharacteristic
89C4⋊C4×D47C2×C411yescharacteristic
90C4⋊C4×D47C2×C411yescharacteristic
91C4⋊C4×D47C2×C411yescharacteristic
92C2×(C2×D47)⋊C4—21no—
93C22⋊C4×D47—21no—
94C22⋊C4×D47—21no—
95C2×C4×Dic47C2311yescharacteristic
96C42×D47—21no—
97C42×D47—21no—
98#13093959—22no—
99#13093959—22no—
100#13093958C2×C411yescharacteristic
101#13093958C2×C411yescharacteristic
102#13093957C2×C411yescharacteristic
103#13093957C2×C411yescharacteristic
104#13093957C2×C411yescharacteristic
105#13093957C2×C411yescharacteristic
106#13093956C2×C411yescharacteristic
107#13093956C2×C411yescharacteristic
108#13093955C2×C411yescharacteristic
109#13093955C2×C411yescharacteristic
110#13093955C2×C411yescharacteristic
111#13093955C2×C411yescharacteristic
112C4⋊(C47⋊C8)—21no—
113C4⋊(C47⋊C8)—21no—
114Dic47⋊C8—21no—
115Dic47⋊C8—21no—
116Dic47⋊C8—21no—
117Dic47⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8—21no—
120(C2×D47)⋊C8—21no—
121(C2×D47)⋊C8—21no—
122(C2×D47)⋊C8D411yescharacteristic
123(C2×D47)⋊C8D411yescharacteristic
124(C2×D47)⋊C8D411yescharacteristic
125(C2×D47)⋊C8D411yescharacteristic
126#13093935—21no—
127#13093935—22no—
128#13093934—21no—
129#13093934—21no—
130C4×C47⋊C8—21no—
131C8×Dic47—21no—
132C8×Dic47—21no—
133C8×Dic47—22no—
134C47⋊#95—21no—
135C2×M16×C47C2311yescharacteristic
136C2×M16×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C22×C8×C47C2311yescharacteristic
139#117×C47C2311yescharacteristic
140#117×C47C2311yescharacteristic
141C2×C42×C47C2311yescharacteristic
142#107×C47C2×C411yescharacteristic
143#107×C47C2×C411yescharacteristic
144#106×C47C2×C411yescharacteristic
145#106×C47C2×C411yescharacteristic
146C4⋊C8×C47—21no—
147C4⋊C8×C47—21no—
148#97×C47—21no—
149C4×C8×C47—21no—
150C23×D47#4111yescharacteristic
151C22×C4×C47—21no—
152C22×C4×C47C2411yescharacteristic
153C22×Dic47—21no—
154C22×Dic47#4111yescharacteristic
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—21no—
163C2×C4×D47C22×C411yescharacteristic
164C2×C4×D47C22×C411yescharacteristic
165C2×C4×D47C2×D411yescharacteristic
166C2×C4×D47C2×D411yescharacteristic
167M16×C47—21no—
168M16×C47—21no—
169M16×C47—21no—
170M16×C47—21no—
171C2×C8×C47—21no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47—21no—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C2×C8×C47C22×C411yescharacteristic
178C2×C8×C47C22×C411yescharacteristic
179C2×C8×C47C2×D411yescharacteristic
180C2×C8×C47C2×D411yescharacteristic
181C4⋊C4×C47C22×C411yescharacteristic
182C4⋊C4×C47C22×C411yescharacteristic
183C4⋊C4×C47C22×C411yescharacteristic
184C4⋊C4×C47C22×C411yescharacteristic
185C22⋊C4×C47—21no—
186C22⋊C4×C47—21no—
187C42×C47—21no—
188C42×C47—21no—
189C42×C47—21no—
190C42×C47—21no—
191C22⋊Dic47—21no—
192C22⋊Dic47—21no—
193(C2×D47)⋊C4—21no—
194(C2×D47)⋊C4—21no—
195(C2×D47)⋊C4—21no—
196(C2×D47)⋊C4—21no—
197(C2×D47)⋊C4—42no—
198C4⋊Dic47C22×C411yescharacteristic
199C4⋊Dic47C22×C411yescharacteristic
200C4⋊Dic47C22×C411yescharacteristic
201C4⋊Dic47C22×C411yescharacteristic
202Dic47⋊C4—21no—
203Dic47⋊C4—21no—
204Dic47⋊C4—21no—
205Dic47⋊C4—21no—
206C4×Dic47—21no—
207C4×Dic47—21no—
208C4×Dic47—21no—
209C4×Dic47—21no—
210C4×Dic47—21no—
211C4×Dic47—21no—
212C4×Dic47—21no—
213C4×Dic47—21no—
214#10625329—21no—
215#10625329—21no—
216#10625329—21no—
217#10625329—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8C22×C411yescharacteristic
223C2×C47⋊C8C22×C411yescharacteristic
224C2×C47⋊C8C2×D411yescharacteristic
225C2×C47⋊C8C2×D411yescharacteristic
226C2×C47⋊C8#4112yes—
227C2×C47⋊C8#4112yes—
228#10625324—22no—
229#10625324—22no—
230#10625324—22no—
231#10625324—22no—
232C23×C47C2×#4111yescharacteristic
233C22×D47—21no—
234C22×D47—21no—
235C22×D47—41no—
236C22×D47—41no—
237C22×D47C4×D411yescharacteristic
238C22×D47C4×D411yescharacteristic
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47C23×C411yescharacteristic
247C2×C4×C47C22×D411yescharacteristic
248C2×C4×C47C2×#4111yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C472−1+411yescharacteristic
251C2×C4×C472−1+411yescharacteristic
252C2×Dic47—21no—
253C2×Dic47—21no—
254C2×Dic47—22no—
255C2×Dic47—21no—
256C2×Dic47—21no—
257C2×Dic47—21no—
258C2×Dic47—21no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47C4×D411yescharacteristic
262C2×Dic47C4×D411yescharacteristic
263C4×D47—21no—
264C4×D47—21no—
265C4×D47—21no—
266C4×D47—21no—
267C4×D47—21no—
268C4×D47—21no—
269C4×D47—21no—
270C4×D47—21no—
271C4×D47—42no—
272C4×D47—42no—
273C4×D47—81no—
274C4×D47—81no—
275C8×C47—21no—
276C8×C47—21no—
277C8×C47—21no—
278C8×C47—21no—
279C8×C47—41no—
280C8×C47—41no—
281C47⋊C8—21no—
282C47⋊C8—21no—
283C47⋊C8—41no—
284C47⋊C8—41no—
285C47⋊C8#11712yes—
286C47⋊C8#11712yes—
287#22608—471nomaximal, Sylow
288C22×C47—21no—
289C22×C47—21no—
290C22×C47C2×C4×D411yescharacteristic
291C22×C47#55211yescharacteristic
292C22×C47#55211yescharacteristic
293C2×D47—21no—
294C2×D47—21no—
295C2×D47—21no—
296C2×D47—21no—
297C2×D47—21no—
298C2×D47—21no—
299C2×D47—81no—
300C2×D47—81no—
301C4×C47—41no—
302C4×C47—41no—
303C4×C47—41no—
304C4×C47—41no—
305C4×C47—81no—
306C4×C47C2×#11711yescharacteristic
307C4×C47#51911yescharacteristic
308C4×C47#54711yescharacteristic
309C4×C47#54711yescharacteristic
310Dic47—21no—
311Dic47—21no—
312Dic47—42no—
313Dic47—41no—
314Dic47—41no—
315Dic47—41no—
316Dic47—41no—
317#2924—471no—
318#2924—471no—
319#2911—471no—
320#1946—471no—
321#1945—471no—
322#1922—471no—
323#1922—471no—
324#1922—471no—
325#1922D4711yescharacteristic, complemented
326#1826—471no—
327#1826—471no—
328#1811—471no—
329#1773—471no—
330#1772—471no—
331#1753—471no—
332C2×C47—21no—
333C2×C47—21no—
334C2×C47#234411yescharacteristic
335C2×C47#295511yescharacteristic
336C2×C47#295611yescharacteristic
337D47—41no—
338D47—41no—
339C22×M16—471no—
340C2×#117—471no—
341C2×#117—471no—
342#433—941no—
343#433—941no—
344#433—941no—
345#433—941no—
346#432—941no—
347#432—941no—
348#431—941no—
349#431—941no—
350C2×#108—471no—
351C2×#108—471no—
352#428—471no—
353#428—471no—
354#428—471no—
355#428—471no—
356#428—471no—
357#428—471no—
358#428—471no—
359#428—471no—
360#427—471no—
361#427—471no—
362#427—471no—
363#427C2×D4711yescharacteristic
364#424—471no—
365#424—471no—
366#424—471no—
367#424C2×D4711yescharacteristic
368#407—471no—
369#407—471no—
370C2×C22⋊C8—471no—
371#405—471no—
372#405—471no—
373#405—471no—
374#405C2×D4711yescharacteristic
375C2×#97—471no—
376C2×C4×C8—471no—
377C4×C22⋊C4—471no—
378#341—471no—
379#341C2×D4711yescharacteristic
380#339—471no—
381#339—471no—
382#339—471no—
383#339—471no—
384#339—471no—
385#339—471no—
386#339C2×D4711yescharacteristic
387#339C2×D4711yescharacteristic
388#336—471no—
389#336C2×D4711yescharacteristic
390C47#2260811yescharacteristic, complemented, Sylow
391C23×C4—471no—
392C2×M16—471no—
393C2×M16—471no—
394C2×M16—471no—
395C2×M16—471no—
396C2×M16—471no—
397C2×M16—471no—
398C2×M16—942no—
399C2×M16—942no—
400C2×M16C22×D4711yescharacteristic
401C2×M16C22×D4711yescharacteristic
402C22×C8—471no—
403C22×C8—471no—
404C22×C8C22×D4711yescharacteristic
405C22×C8C22×D4711yescharacteristic
406#117—471no—
407#117—471no—
408#117—471no—
409#117—471no—
410#117—471no—
411#117—471no—
412#117—941no—
413#117—941no—
414#117—941no—
415#117—941no—
416#117C22×D4711yescharacteristic
417#117C22×D4711yescharacteristic
418C2×C4⋊C4—471no—
419C2×C4⋊C4—471no—
420C2×C4⋊C4—471no—
421C2×C4⋊C4—471no—
422C2×C22⋊C4—941no—
423C2×C22⋊C4—941no—
424C2×C22⋊C4—941no—
425C2×C42—471no—
426C2×C42—941no—
427C2×C42—941no—
428C2×C42C22×D4711yescharacteristic
429#108—942no—
430#108—942no—
431#107—471no—
432#107—471no—
433#107—471no—
434#107—471no—
435#107—471no—
436#107—471no—
437#107C4×D4711yescharacteristic
438#107C4×D4711yescharacteristic
439#106—471no—
440#106—471no—
441#106—471no—
442#106—471no—
443#106—471no—
444#106—471no—
445#106C4×D4711yescharacteristic
446#106C4×D4711yescharacteristic
447C4⋊C8—21no—
448C4⋊C8—21no—
449C4⋊C8—941no—
450C4⋊C8—941no—
451C4⋊C8—941no—
452C4⋊C8—941no—
453C4⋊C8—941no—
454C4⋊C8—941no—
455C22⋊C8—471no—
456C22⋊C8—471no—
457C22⋊C8—471no—
458C22⋊C8—471no—
459C22⋊C8—941no—
460C22⋊C8—941no—
461C22⋊C8—941no—
462C22⋊C8—941no—
463#97—21no—
464#97—942no—
465#97—941no—
466#97—941no—
467#97—941no—
468C4×C8—21no—
469C4×C8—941no—
470C4×C8—942no—
471C4×C8—941no—
472C4×C8—941no—
473#95—941no—
474C24—471no—
475C22×C4—21no—
476C22×C4—471no—
477C22×C4—471no—
478C22×C4—471no—
479C22×C4—471no—
480C22×C4—471no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4—941no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4—941no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4C23×D4711yescharacteristic
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—942no—
496M16—942no—
497M16—942no—
498M16—942no—
499M16—941no—
500M16—941no—
501M16—941no—
502M16—941no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—471no—
510C2×C8—471no—
511C2×C8—472no—
512C2×C8—472no—
513C2×C8—471no—
514C2×C8—471no—
515C2×C8—941no—
516C2×C8—941no—
517C2×C8—941no—
518C2×C8—941no—
519C2×C8C2×C4×D4711yescharacteristic
520C2×C8C2×C4×D4711yescharacteristic
521C2×C8D4×D4711yescharacteristic
522C2×C8D4×D4711yescharacteristic
523C4⋊C4—471no—
524C4⋊C4—471no—
525C4⋊C4—471no—
526C4⋊C4—471no—
527C4⋊C4—941no—
528C4⋊C4—941no—
529C4⋊C4—941no—
530C4⋊C4—941no—
531C4⋊C4C2×C4×D4711yescharacteristic
532C4⋊C4C2×C4×D4711yescharacteristic
533C4⋊C4C2×C4×D4711yescharacteristic
534C4⋊C4C2×C4×D4711yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—941no—
538C22⋊C4—941no—
539C22⋊C4—941no—
540C22⋊C4—941no—
541C22⋊C4—941no—
542C22⋊C4—941no—
543C22⋊C4—1882no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—941no—
549C42—941no—
550C42—941no—
551C42—941no—
552C42—941no—
553C42—941no—
554C42—941no—
555C42—941no—
556C23—471no—
557C23—471no—
558C23—941no—
559C23—941no—
560C23—1881no—
561C23—1881no—
562C23#41×D4711yescharacteristic
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—471no—
571C2×C4—471no—
572C2×C4—941no—
573C2×C4—941no—
574C2×C4—941no—
575C2×C4—941no—
576C2×C4—941no—
577C2×C4—941no—
578C2×C4—941no—
579C2×C4—941no—
580C2×C4—941no—
581C2×C4—941no—
582C2×C4—942no—
583C2×C4—941no—
584C2×C4—941no—
585C2×C4—941no—
586C2×C4—941no—
587C2×C4—3761no—
588C2×C4—3761no—
589C2×C4—1882no—
590C2×C4—1882no—
591C2×C4—1881no—
592C2×C4—1881no—
593C2×C4C22×C4×D4711yescharacteristic
594C2×C4C2×D4×D4711yescharacteristic
595C2×C4#41×D4711yescharacteristic
596C2×C4#41×D4711yescharacteristic
597C2×C4#1309407111yescharacteristic
598C2×C4#1309407211yescharacteristic
599C8—21no—
600C8—21no—
601C8—21no—
602C8—21no—
603C8—41no—
604C8—41no—
605C8—472no—
606C8—472no—
607C8—941no—
608C8—941no—
609C8—1881no—
610C8—1881no—
611C22—21no—
612C22—21no—
613C22—941no—
614C22—941no—
615C22—941no—
616C22—941no—
617C22—941no—
618C22—941no—
619C22—3761no—
620C22—3761no—
621C22C4×D4×D4711yescharacteristic
622C22#1568980511yescharacteristic
623C22#1568980911yescharacteristic
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—81no—
629C4—941no—
630C4—941no—
631C4—1882no—
632C4—1881no—
633C4—1881no—
634C4—1881no—
635C4—1881no—
636C4#117×D4711yescharacteristic
637C4#1568959911yescharacteristic
638C4#1568977111yescharacteristic
639C4#1568977511yescharacteristic
640C2—21no—
641C2—21no—
642C2—1881no—
643C2—1881no—
644C2#2024625411yescharacteristic
645C2#2025228611yescharacteristic
646C2#2025229611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1922C2
socleC22×C47C2×C4×D4
prime radicalC23×D47#41
cosocleC22×C4×C47C24
hypercenter#1922D47
hypocenterC47#22608
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. #20244140C2semidirect
5. #20244133C2semidirect
6. #20243989C2semidirect
7. #20243988C2semidirect
8. #20243986C2semidirect
12. #20243271C2semidirect
13. #20243268C2semidirect
15. C47×#1922C2semidirect
29. #15689164C4semidirect
30. #15689164C4semidirect
31. #15689164C4semidirect
32. #15689164C4semidirect
33. #15689162C4semidirect
34. #15689162C4semidirect
35. #15689162C4semidirect
36. #15689162C4semidirect
325. #1922D47semidirect
390. C47#22608semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202520452
#202520432
#202519762
#202441402
#202441332
#202439892
#202439882
#202439862
#202434862
#202434292
#202432712
#202432682
#202431702
C47×#19222
#2260847